On the other hand, by including a low-entropy condition, here we are able to work globally in space-time. This allows for significantly simplified arguments. In fact, the key observation of this paper is that in this setting one can completely avoid the classification of one-sided ancient flows and instead rely on a soft argument based on compactness and a new geometric property of non-generic shrinkers (see Proposition REF ). We emphasize that a drawback of the methods used in this note as compared to our previous work is that the arguments used here give no indication as to the local dynamics near a non-generic singularity (such information was obtained in [1]} near asymptotically conical and compact shrinkers; see also [2]}, [3]}).
